Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Calculator

✖Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis.ⓘ Initial Angular Velocity [ω_o]			+10% -10%
✖Time Taken to Travel the Path is the duration required for an object to move from one point to another along a specific path or trajectory.ⓘ Time Taken to Travel the Path [t]			+10% -10%
✖Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.ⓘ Angular Acceleration [α]			+10% -10%

✖Angular Displacement is the angle through which an object rotates about a fixed axis, describing the change in its orientation.ⓘ Angular Displacement given Initial Angular Velocity Angular Acceleration and Time [θ]

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Angular Displacement given Initial Angular Velocity Angular Acceleration and Time

Formula

θ = ω o \cdot t + \frac{α \cdot t^{2}}{2}

Example

120 rad = 15.2 rad/s \cdot 6 s + \frac{1.6 rad/s² \cdot {6 s}^{2}}{2}

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Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
θ = ω_o*t+(α*t^2)/2
This formula uses 4 Variables

Variables Used

Angular Displacement - (Measured in Radian) - Angular Displacement is the angle through which an object rotates about a fixed axis, describing the change in its orientation.
Initial Angular Velocity - (Measured in Radian per Second) - Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis.
Time Taken to Travel the Path - (Measured in Second) - Time Taken to Travel the Path is the duration required for an object to move from one point to another along a specific path or trajectory.
Angular Acceleration - (Measured in Radian per Square Second) - Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.

STEP 1: Convert Input(s) to Base Unit

Initial Angular Velocity: 15.2 Radian per Second --> 15.2 Radian per Second No Conversion Required
Time Taken to Travel the Path: 6 Second --> 6 Second No Conversion Required
Angular Acceleration: 1.6 Radian per Square Second --> 1.6 Radian per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = ω_o*t+(α*t^2)/2 --> 15.2*6+(1.6*6^2)/2

Evaluating ... ...

θ = 120

STEP 3: Convert Result to Output's Unit

120 Radian --> No Conversion Required

FINAL ANSWER

120 Radian <-- Angular Displacement

(Calculation completed in 00.004 seconds)

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< Kinematics Calculators

Final Angular Velocity given Initial Angular Velocity Angular Acceleration and Time

Go Final Angular Velocity = Initial Angular Velocity+Angular Acceleration*Time Taken to Travel the Path

Final Velocity of Body

Go Final Velocity = Initial Velocity+Acceleration of Body*Time Taken to Travel the Path

Final Velocity of Freely Falling Body from Height when it Reaches Ground

Go Velocity on Reaching Ground = sqrt(2*Acceleration due to Gravity*Height of Crack)

Normal Acceleration

Go Normal Acceleration = Angular Velocity^2*Radius of Curvature

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time Formula

Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
θ = ω_o*t+(α*t^2)/2

What is Angular Displacement ?

The angular displacement of a body is the angle in radians (degrees, revolutions) through which a point revolves around a center or line that has been rotated in a specified sense about a specified axis. When a body rotates about its axis, the motion cannot simply be analyzed as a particle, as in circular motion it undergoes a changing velocity and acceleration at any time (t). When dealing with the rotation of a body, it becomes simpler to consider the body itself rigid

How to Calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time calculator uses Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2 to calculate the Angular Displacement, Angular Displacement given Initial Angular Velocity Angular Acceleration and Time formula is defined as a measure of the change in angular position of an object undergoing rotational motion, considering the initial angular velocity, angular acceleration, and time of motion. Angular Displacement is denoted by θ symbol.

How to calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time using this online calculator? To use this online calculator for Angular Displacement given Initial Angular Velocity Angular Acceleration and Time, enter Initial Angular Velocity (ω_o), Time Taken to Travel the Path (t) & Angular Acceleration (α) and hit the calculate button. Here is how the Angular Displacement given Initial Angular Velocity Angular Acceleration and Time calculation can be explained with given input values -> 112.8 = 15.2*6+(1.6*6^2)/2.

FAQ

What is Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time formula is defined as a measure of the change in angular position of an object undergoing rotational motion, considering the initial angular velocity, angular acceleration, and time of motion and is represented as θ = ω_o*t+(α*t^2)/2 or Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2. Initial Angular Velocity is the velocity of an object at the start of its motion, describing its initial rotational motion around a fixed axis, Time Taken to Travel the Path is the duration required for an object to move from one point to another along a specific path or trajectory & Angular Acceleration is the rate of change of angular velocity, describing how fast the rotation of an object changes over time.

How to calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time?

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time formula is defined as a measure of the change in angular position of an object undergoing rotational motion, considering the initial angular velocity, angular acceleration, and time of motion is calculated using Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2. To calculate Angular Displacement given Initial Angular Velocity Angular Acceleration and Time, you need Initial Angular Velocity (ω_o), Time Taken to Travel the Path (t) & Angular Acceleration (α). With our tool, you need to enter the respective value for Initial Angular Velocity, Time Taken to Travel the Path & Angular Acceleration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angular Displacement?

In this formula, Angular Displacement uses Initial Angular Velocity, Time Taken to Travel the Path & Angular Acceleration. We can use 3 other way(s) to calculate the same, which is/are as follows -

Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
Angular Displacement = ((Initial Angular Velocity+Final Angular Velocity)/2)*Time Taken to Travel the Path
Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration)

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